Impact of Secondary MAC Cooperaton on Spectrum Sharng n Cogntve ado Networks Tarq Elkourd and Osvaldo Smeone CWCSP, ECE Dept. New Jersey Insttute of Technology Unversty Heghts, Newark, New Jersey 0702 Emal: the3@njt.edu, osvaldo.smeone@njt.edu Abstract In ths paper, the mpact of secondary MAC cooperaton on the sum-throughput of multchannel cogntve rado networks s studed. The man goal s twofold: Gven the prmary and secondary users' duty cycle, () nvestgate the amount of spectrum sharng (.e., number of secondary users) that maxmzes the sum-throughput n the presence of secondary MAC cooperaton; () assess the performance gans attanable wth cooperaton. Frst, analyss s provded for the dealstc case of perfect sensng, wth a smple model for secondary cooperaton. Then, for the more realstc case of mperfect sensng, novel cooperatve secondary strateges are proposed that are shown to provde relevant performance gans n terms of sum-throughput. Fnally, numercal smulaton results are provded to evaluate the performance of the cooperatve schemes relatve to other noncooperatve schemes. I. INTODUCTION The need to accommodate fast-emergng wreless communcaton servces has motvated academa and ndustry to look for a soluton to the problem of avalable spectrum scarcty. In fact, recent studes on regulated spectrum access show that most of the allocated spectrum fragments are underutlzed both temporally and spatally []-[2]. Concepts such as spectrum sharng and opportunstc spectrum access, and more generally cogntve rado, were ntroduced as possble solutons (see, e.g., [3]-[4]). Cogntve rado has the potentalty to overcome the spectral shortage by enablng secondary (unlcensed) users to utlze spectrum holes left open by the prmary nactvty. Secondary (or cogntve) rados are typcally envsoned to employ a "sense-before-talk" strategy that prescrbes channel access based on spectrum sensng for detecton of spectrum holes. The lmts of such an approach have been recently studed both n terms of sensng accuracy and overall throughput (see, e.g., [5]). It has been concluded that cooperaton among the secondary nodes at physcal and/or MAC layers s necessary to guarantee effectve secondary spectrum access. For nstance, reference [6] (see also references theren) shows that relevant gans n terms of secondary detector senstvty can be accrued by deployng cooperatve sensng at the physcal layer, whle [7] ponts to the advantages of MAC secondary cooperaton. In ths paper, we are nterested n extendng the consderatons mentoned above to the spectrum sharng multchannel scenaro studed n [8] (see Fg. ). In ths model, the network desgner s faced wth the ssue of optmzng the number of Fg.. A cogntve rado network: N p prmary and N s secondary users are unformly dstrbuted on a dsc of radus. Each actve prmary node transmts on ts own subchannel, whle secondary nodes employ a lstenbefore-talk mechansm over all subchannels for opportunstc spectrum access [8]. secondary users versus the number of avalable subchannels and prmary users n order to optmze the system throughput gven the prmary and secondary trafc duty cycle. eference [8] studes the trade-off at hand between regulaton (more prmary users) and autonomy (more secondary users) n the absence of cooperaton among the secondary users. Ths paper, nstead, studes the mpact of secondary MAC cooperaton on the throughput of the dscussed spectrum sharng system. Followng [8], we rst consder an dealstc system wth perfect sensng and a smple model for cooperaton to gan analytcal nsght nto the mpact of secondary cooperaton (Sec. II). Ths s followed by the study of a more realstc model wth mperfect sensng and practcal cooperaton schemes (Sec. III), for whch numercal results and comparson to the noncooperatve case [8] are provded n Sec. IV. II. PEFECT SENSING, COLLISION MODEL, SIMPLE COOPEATION MODEL We consder the network model n [8] wheren a frequency band s equally dvded nto N p subchannels, each assgned to one of N p prmary users, and tme-slotted. The frequency band s also shared opportunstcally among N s secondary users for hgher bandwdth efcency. Prmary and secondary users are located on a crcle of radus n a unform dstrbuton fashon as shown n Fg.. For analytcal smplcty, we assume that prmary and secondary users are actve (backlogged) ndependently wth equal duty The terms user and node-par (transmtter-recever par) are used nterchangeably n ths context.
cycle (trafc generaton probablty) p (0 p ) n each tme slot. Prmary users transmt whenever they are actve, whereas actve secondary users access the subchannels only f deemed dle from prmary transmssons. We extend the analyss n [8], where no cooperaton was consdered, by assessng the potental gans of secondary cooperaton over the non-cooperatve case. To smplfy the analyss, we consder, at rst, as n [8], perfect sensng (.e., all secondary users can detect unoccuped channels wth no errors), and a collson model where a transmsson s successful only n the absence of nterference. Furthermore, we assume a smple model for cooperaton n whch all the secondary users n a gven area of "cooperaton radus" coop can perfectly cooperate, thus avodng collsons (see detals below). We now evaluate the average system sum-throughput, followng the same basc notaton of [8]. Denng as C the rate n bps/hz of each packet transmsson, t s easy to see that the prmary users' sum-throughput Cp sum can be expressed as Cp sum = CN p p, whle the secondary users' sum-throughput depends on the current number of free subchannels and can be wrtten as N X p Cs sum Np = p Np ( p) Cs sum (). () = In (), Cs sum () represents the secondary sum-throughput condtoned on the number of avalable subchannels, whch reads Cs sum () = P N s N s j= j p j ( p) Ns j Cs sum (; j), where the average secondary sum-throughput when j secondary users are actve over avalable (prmary) subchannels can be wrtten as follows " X # Cs sum (; j) = CE G k = C E [G k ]. (2) k= In (2), G k s an ndcator varable that equals one f the k th subchannel s successfully used by one of the j actve secondary users, and zero otherwse. In [8], (2) s evaluated to Cs sum j (; j) = Cj n the absence of secondary cooperaton. In order to evaluate (2) (and thus the sum-throughput) wth secondary cooperaton, here we consder the followng smple model for cooperaton. Each secondary user at rst selects one of the avalable subchannels randomly wth probablty =. The overall system regon (of area 2, where s the radus of the total area) s dvded nto "cooperatve zones" of area coop 2 n an arbtrary fashon. We assume that users wthn the same zone (that have selected the same subchannel) can perfectly cooperate before transmsson so that only one such user wll attempt transmsson on the gven subchannel. As shown n the Appendx, we have C sum s (; j) = C l=2 " j j l j + (3) l j l # 2l coop. Fg. 3. The cogntve rado network of Fg. wth mperfect sensng, nterference model, and local cooperaton. Secondary node-pars detect actve prmary transmtters only wthn ther sensng regons of radus s and are able to communcate wth other secondary neghbors wthn the cooperaton regon of radus coop. so that the overall sum-throughput C sum can be expressed as " C sum = CN p p + XNp Np p Np ( p) N p = p p Ns 2 coop N s + p + p coop 2 Ns p ## (4) Ns. It s noted that for coop = 0 (no cooperaton) equaton (4) reduces to the sum-throughput derved n [8] (see (4) theren). Fg. 2(a) shows the sum-throughput (4) normalzed as C sum =CN p n packets=(tme-slotsubchannel) versus the number of secondary users N s for N p = 9 and p = 0:. For comparson, we plot the non-cooperatve case coop = 0 for reference. It can be seen that the sum-throughput along wth the optmal number of secondary users Ns ncrease as the cooperaton radus coop ncreases. In the lmt, for the case coop =, a sufcently large number of secondary users N s allows a full normalzed sum-throughput of to be obtaned. Fg. 2(b) plots the normalzed sum-throughput C sum =CN p versus the number of secondary users N s for a larger trafc generaton probablty p = 0:25. We notce that ncreasng the probablty p decreases the optmal number of secondary users for the same cooperaton radus coop due to smaller number of average avalable slots and larger secondary packet generaton probablty. Furthermore, smlar gans as the prevous case can be realzed. III. IMPEFECT SENSING, INTEFEENCE MODEL, LOCAL COOPEATION The dscusson n the prevous secton has shown that large sum-throughput gans can n prncple be attaned va MAC secondary cooperaton. Here, we consder more realstc assumptons on sensng and channel model followng Sec. III of [8]: () mperfect sensng: a secondary user can detect prmary transmtters only wthn a sensng radus s around the user tself (see Fg. 3); () nterference model: prmary and secondary transmtters and recevers are randomly located n a crcular area of radus. Subchannel gans are determned by a path loss model as jh mn j 2 = =d mn where d mn s the dstance between the transmttng node m and recevng node
(a) Normalzed sum-throughput C sum =CN p versus number of secondary users N s for perfect sensng, collson model, smple cooperaton (p = 0:; N p = 9): (b) Normalzed sum-throughput C sum =CN p versus number of secondary users N s for perfect sensng, collson model, smple cooperaton (p = 0:25; N p = 9): Fg. 2. Fgures 2(a) and 2(b) plot the sum-throughput C sum = CN p versus the ncreasng number of secondary users N s for dfferent values of cooperaton rad coop for duty cycles p = 0: and p = 0:25 respectvely. n and s the path loss exponent. The sgnal-to-nterferenceplus-nose rato (SIN) on an actve lnk m n on subchannel k s gven by jh mn j 2 P SIN mn;k = + P jh n j 2 P, (5) 2B k ;6=m where the sum runs over the set B k of prmary and secondary transmtters actve on the kth subchannel, and P represents the (equal) transmtted energy per symbol (Joule): Fxed-rate transmssons are attempted by all actve transmtters wth rate mn;k = log + jh mnj 2 P + I! ; (6) where parameter I represents the nterference tolerance [8]. In other words, from (5), a transmsson from m to n s successful P f and only f the aggregate nterference satses jh n j 2 P I. Moreover, rather than consderng 2B k ;6=m deal cooperaton as n Sec. II, we propose MAC cooperaton schemes based on the assumed ablty of each secondary transmtter to broadcast bref "MAC cooperaton messages" to all the actve secondary users only locally, namely wthn a dsc of radus coop around the transmtter tself, at the begnnng of each slot. The objectve of these cooperatve schemes s to ncrease the sum-throughput by: (a) mnmzng "collsons" between actve secondary users (as n Sec. II); (b) reducng nterference to actve prmary users (ths was not relevant n Sec. II due to the assumpton of perfect sensng). We propose two cooperatve schemes, the rst based on a one-shot message exchange (and amed at (b)) and the second on a two-shot strategy (amed at both (a) and (b)). A. One-Shot Cooperaton Scheme In ths cooperaton scheme, we ntroduce a sngle subtmeslot at the begnnng of each tme-slot where each actve secondary node broadcasts only one cooperaton message to all secondary neghbors wthn ts cooperaton regon. Each actve secondary node j scans the bandwdth for spectrum holes and generates a "subchannel avalablty vector" Z j of bnary varables Z j = I[the th subchannel s detected as avalable by the jth user], where I[] s the ndcator functon. Ths vector Z j s broadcast to all secondary nodes wthn the cooperaton regon of the jth user. After the end of the broadcast phase, each secondary node sums the receved vectors Z j entry-wse and selects the subchannel k wth the largest entry (tes are resolved arbtrarly). If two or more subchannels have the same largest entry, a secondary node randomly selects one of them for transmsson. Ths strategy bascally reduces the probablty of nterferng wth actve prmary transmtters and can be seen as an mplementaton of cooperatve sensng. B. Two-Shot Cooperaton Scheme Ths cooperaton scheme operates as the prevous, but adds another subtme-slot after the rst one, where actve secondary nodes employ a second MAC message exchange to reduce the nterference to other secondary nodes. Speccally, n the second phase, each actve secondary node broadcasts ts selected subchannel (see dscusson above) to all secondary nodes
(a) One-shot cooperaton scheme. (b) Two-shot cooperaton scheme. Fg. 4. Sum-throughput C sum versus number of secondary users N s for mperfect sensng, nterference model, local cooperaton (I = 0, s = 0:5). (a) One-shot cooperaton scheme. (b) Two-shot cooperaton scheme. Fg. 5. Sum-throughput C sum versus number of secondary users N s for mperfect sensng, nterference model, local cooperaton (I = 2, s = 0:5). wthn ts cooperaton regon. Then, each actve secondary node performs random access, calculatng the transmsson probablty as =l, where l > 0 s the number of neghbors that have reported ther decson as the selected subchannel (for l = 0, we set the probablty to one). Ths strategy provdes an mprovement over the One-shot snce not only t employs cooperatve sensng but also t reduces collsons between actve secondary nodes and therefore ncreases the secondary sum-throughput. C. Smulaton esults In ths secton we explore the benets of the secondary MAC cooperatve schemes proposed above by numercally evaluatng the sum-throughput for N p = 5 prmary users, xed duty cycle p = 0:5 for prmary and secondary users, and sensng radus s = 0:5. Fgures 4 and 5 compare the sum-throughput wth ncreasng number of secondary users N s for dfferent values of the cooperaton radus coop for the one-shot cooperaton and two-shot cooperaton schemes for nterference tolerance I = 0 and I = 2 respectvely and conrms the general conclusons of Sec. II n that cooperaton
Fg. 6. The sum-throughput gan vs. cooperaton radus for One-shot and Two-shot schemes (I = and I = 2). both ncreases the sum-throughput and the optmal number of secondary users Ns. It can be seen from Fg. 4(a) that the sum-throughput ncreases along wth the optmal number of secondary users as we ncrease the cooperaton radus coop. Fg. 4(b) shows the gans n the sum-throughput as the number of secondary users ncreases as a result of applyng random access to the shared subchannel resource n the twoshot strategy. Notce that for coop we have a constant sum-throughput curve 2,.e., no collsons between secondary users, and therefore the two-shot scheme can support a larger number of secondary node-pars. Fg. 5(a) shows that, for the one-shot scheme wth nterference tolerance I = 2, a cooperaton radus coop = 0:5 s more advantageous than larger values, snce coop needs to strke a balance between accuracy of the prmary detecton (large coop ) and explotng the nterference tolerance I > 0 by allowng more secondary transmssons (small coop ). Fg. 5(b) shows agan that the two-shot cooperaton scheme outperforms the one-shot approach especally for larger values of N s due to the ablty to reduce secondary nterference. Notce that the sum-throughput attaned n Fg. 5 s lower than that n Fg 4 for xed N s and coop snce employng hgher nterference tolerance dctates lower transmsson rates. Fg. 6 compares the sum-throughput gan wth ncreasng cooperaton radus coop for I = and I = 2 for the One-shot and the Two-shot cooperaton relatve to non-cooperatve schemes gven a xed number of secondary users N s = 5. It can be seen that the maxmum achevable sum-throughput gan ntermedates the two extremes of full competton ( coop = 0) and full cooperaton ( coop = 2). 2 Notce that here, unlke Sec. II, coop can be larger than one snce we have to condton on the poston of the secondary nodes. IV. CONCLUSIONS Ths paper has shown that, n a multchannel spectrum sharng system, the possblty of exchangng local MAC messages among secondary nodes: () leads to an optmal system desgn that prescrbes a larger number of secondary users (that s, more autonomy and less regulaton); () yelds relevant gans n terms of overall system throughput wth respect to a noncooperatve scenaro. The nterplay between full competton and full cooperaton among the secondary nodes s evdent n the tradeoff between sum-throughput gan maxmzaton and sum-nterference mnmzaton at the recevers. Based on the ntal promsng results n ths paper, future work wll need to address the full desgn of a MAC protocol that support such message exchange n the cogntve scenaro at hand. APPENDIX: POOF OF (3) Let S k be the number of users that select a gven subchannel k and T k be the number of users that attempt transmsson on such subchannel. The probablty that an avalable subchannel k s successfully used by a secondary node can be expressed as E [G k ] = Pr [S k = l] Pr [T k = js k = l] l= = j j + l=2 l j j l where l = Pr [T k = js k = l] : We have = and to calculate P r[t k = js k = l], we observe that ths s the probablty that all the S k users fall wthn the same cooperaton subregon, whch equals (assumng unform user dstrbuton n a dsc of radus ): 2l coop Pr [T k = js k = l] = ; (7) thus concludng the proof. EFEENCES [] Federal Communcatons Commsson Spectrum Polcy Task Force," eport of the Spectrum Efcency Workng Group", FCC, Tech eport, Nov. 2002. [2] Federal Communcatons Commsson, Cogntve ado Technologes Proceedng (CTP), ET Docket No. 03-08, http://www.fcc.gov/oet/cogntverado/ [3] IEEE Intern. Symp. Fronters n Dynamc Spectrum Access Networks, Nov. 2005. [4]. Etkn, A. K. Parekh and D. Tse, Spectrum sharng for unlcensed bands, IEEE Jour. on Select. Areas n Commun., vol. 25, pp. 57 528, Apr. 2007. [5] Q. Zhao, "Spectrum opportunty detecton: how good s lsten-beforetalk?," n Proc. Aslomar Conf. on Sgnals, Systems and Comp., 2007. [6] G. Ganesan and Ye L, Cooperatve spectrum sensng n cogntve rado, Part I: two user networks, IEEE Trans. Wreless Commun., vol. 6, no. 6, pp. 2204-223, June 2007. [7] A. Saha,. Tandra, S.M. Mshra, and N.K.Hoven, Fundamental desgn tradeoffs n cogntve rado systems, n Proc. Internatonal Workshop on Technology and Polcy for Accessng Spectrum (TAPAS 2006). [8] S. Srnvasa, S. A. Jafar, "How much spectrum sharng s optmal n cogntve rado networks?," IEEE Trans. on Wreless Commun., vol. 7, no. 0, pp. 400-408, October 2008. l l;